{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bb5afc1a",
   "metadata": {},
   "source": [
    "# Lab: Central Limit Theorem\n",
    "\n",
    "Welcome! In this ungraded lab see applications of the Central Limit Theorem when working with different distributions of data. You will see how to see the theorem in action, as well as scenarios in which the theorem doesn't hold.\n",
    "\n",
    "Let's get started!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dff173ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n",
    "\n",
    "import utils"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4298763",
   "metadata": {},
   "source": [
    "## Gaussian population\n",
    "\n",
    "Begin with the most straightforward scenario: when your population follows a Gaussian distribution. You will generate the data for this population by using the [np.random.normal](https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html) function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "db0e6232",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 10\n",
    "sigma = 5\n",
    "\n",
    "gaussian_population = np.random.normal(mu, sigma, 100_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bafe463",
   "metadata": {},
   "source": [
    "The population has a mean of 10 and a standard deviation of 5 (since these are the true parameters you used to generate the data) and a total of 100'000 observations. You can visualize its histogram by running the next cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "aa13b407",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(gaussian_population, stat=\"density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dffb432",
   "metadata": {},
   "source": [
    "## Sampling from the population\n",
    "\n",
    "Since this lab uses simulated data you could very easily use the whole population to draw conclusions from the data. For instance if you didn't know about the values of $\\mu$ and $\\sigma$ you could get very close estimates of the true values by computing the mean and standard deviation of the whole population like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d77f1985",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian population has mean: 10.0 and std: 5.0\n"
     ]
    }
   ],
   "source": [
    "gaussian_pop_mean = np.mean(gaussian_population)\n",
    "gaussian_pop_std = np.std(gaussian_population)\n",
    "\n",
    "print(f\"Gaussian population has mean: {gaussian_pop_mean:.1f} and std: {gaussian_pop_std:.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "774ec0e3",
   "metadata": {},
   "source": [
    "However in real life this will most certainly not be possible and you will need to use samples that are nowhere near as big as the population to draw conclusions of the behaviour of the data.  After all, this is what statistics is all about.\n",
    "\n",
    "Depending on the sampling techniques you could encounter different properties, this is where the Central Limit Theorem comes in handy. For many distributions the following is true:\n",
    "\n",
    "The sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution, regardless of the distribution of the individual variables themselves. This is important because the normal distribution is well-understood and allows for statistical inference and hypothesis testing.\n",
    "\n",
    "With this in mind you need a way of averaging samples out of your population. For this the `sample_means` is defined:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "996fd8ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_means(data, sample_size):\n",
    "    # Save all the means in a list\n",
    "    means = []\n",
    "\n",
    "    # For a big number of samples\n",
    "    # This value does not impact the theorem but how nicely the histograms will look (more samples = better looking)\n",
    "    for _ in range(10_000):\n",
    "        # Get a sample of the data WITH replacement\n",
    "        sample = np.random.choice(data, size=sample_size)\n",
    "\n",
    "        # Save the mean of the sample\n",
    "        means.append(np.mean(sample))\n",
    "\n",
    "    # Return the means within a numpy array\n",
    "    return np.array(means)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19fec648",
   "metadata": {},
   "source": [
    "Let's break down the function above:\n",
    "\n",
    "- You take random samples out of the population (the sampling is done with replacement, which means that once you select an element you put it back in the sampling space so you could choose a particular element more than once). This ensures that the independence condition is met.\n",
    "\n",
    "- Compute the mean of each sample\n",
    "\n",
    "- Save the means of each sample in a numpy array\n",
    "\n",
    "The theorem states that if a large enough `sample_size` is used (usually bigger than 30) then the distribution of the sample means should be Gaussian. See it in action by running the next cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "07799fb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the sample means\n",
    "gaussian_sample_means = sample_means(gaussian_population, sample_size=5)\n",
    "\n",
    "# Plot a histogram of the sample means\n",
    "sns.histplot(gaussian_sample_means, stat=\"density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0f7829f",
   "metadata": {},
   "source": [
    "The distribution of the sample means looks pretty Gaussian. However this is not good enough to determine if the theorem holds, after all you used a very small `sample_size` in this example. There are various ways to check if the sample means do follow a Gaussian distribution.\n",
    "\n",
    "The first one is to compute the theoretical $\\mu$ and $\\sigma$ of the sample means which will be denoted with the symbols $\\mu_{\\bar{X}}$ and $\\sigma_{\\bar{X}}$ respectively. These values can be computed as follows:\n",
    "\n",
    "- $\\mu_{\\bar{X}} = \\mu$\n",
    "\n",
    "\n",
    "- $\\sigma_{\\bar{X}} = \\frac{\\sigma}{\\sqrt{n}}$\n",
    "\n",
    "**Note: In this case $n$ is the size of the sample.**\n",
    "\n",
    "And then use these values to plot a Gaussian curve with parameters $\\mu_{\\bar{X}}$ and $\\sigma_{\\bar{X}}$. If the theorem holds then the resulting distribution of the sample means should resemble this Gaussian curve. Run the next cell to include this into the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fa1b3ff2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute estimated mu\n",
    "mu_sample_means = mu\n",
    "\n",
    "# Compute estimated sigma\n",
    "# 5 is being used because you used a sample size of 5\n",
    "sigma_sample_means = sigma / np.sqrt(5)\n",
    "\n",
    "# Define the x-range for the Gaussian curve (this is just for plotting purposes)\n",
    "x_range = np.linspace(min(gaussian_sample_means), max(gaussian_sample_means), 100)\n",
    "\n",
    "# Plot everything together\n",
    "sns.histplot(gaussian_sample_means, stat=\"density\")\n",
    "plt.plot(\n",
    "    x_range,\n",
    "    norm.pdf(x_range, loc=mu_sample_means, scale=sigma_sample_means),\n",
    "    color=\"black\",\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e33c158",
   "metadata": {},
   "source": [
    "They look pretty similar. However you can go one step further and plot a smooth function that attempts to estimate the probability density function of the sample means through a method known as `kernel density estimation`. If this smooth function resembles the Gaussian function then you know that the distribution of the sample means is very similar to a Gaussian:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a315905d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of sample means (blue)\n",
    "sns.histplot(gaussian_sample_means, stat=\"density\", label=\"hist\")\n",
    "\n",
    "# Estimated PDF of sample means (red)\n",
    "sns.kdeplot(\n",
    "    data=gaussian_sample_means,\n",
    "    color=\"crimson\",\n",
    "    label=\"kde\",\n",
    "    linestyle=\"dashed\",\n",
    "    fill=True,\n",
    ")\n",
    "\n",
    "# Gaussian curve with estimated mu and sigma (black)\n",
    "plt.plot(\n",
    "    x_range,\n",
    "    norm.pdf(x_range, loc=mu_sample_means, scale=sigma_sample_means),\n",
    "    color=\"black\",\n",
    "    label=\"gaussian\",\n",
    ")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9564547c",
   "metadata": {},
   "source": [
    "Both curves look almost identical!\n",
    "\n",
    "Another way of checking for normality is to perform a QQ plot of the sample means. The points in this plot should resemble a straight line if the distribution of the data is Gaussian:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "62f22356",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the QQ plot\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "res = stats.probplot(gaussian_sample_means, plot=ax, fit=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a195c31",
   "metadata": {},
   "source": [
    "The resulting QQ plot yields an almost perfect straight line which further confirms that the sample means do follow a Gaussian distribution.\n",
    "\n",
    "Now, put everything together in an interactive widget to experiment with different values for $\\mu$, $\\sigma$ and `sample_size`. **To update the plots you will need to click the `Run Interact` button after changing the parameters**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b0f89d4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "632a75a45eaf4625b13beda59b8b5e5c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=10.0, continuous_update=False, description='mu', max=50.0, min=0.01, r…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.gaussian_clt()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a77283f",
   "metadata": {},
   "source": [
    "Even with very small values for `sample_size` the sample means follow a Gaussian distribution. This is actually one of the properties of the Gaussian distribution so the theorem is not as powerful in this case, since it will always hold regardless of the size of the sample.\n",
    "\n",
    "Now test the theorem with other distributions!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfa5768e",
   "metadata": {},
   "source": [
    "## Binomial Population\n",
    "\n",
    "Now try with a population distribution that is not Gaussian. One such distribution is the Binomial distribution which you already saw covered in the lectures. To generate data that follows this distribution you will need to define values for the parameters of `n` and `p`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ef8c99cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 5\n",
    "p = 0.8\n",
    "\n",
    "binomial_population = np.random.binomial(n, p, 100_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c733da4",
   "metadata": {},
   "source": [
    "The population has a total of 100'000 observations. You can visualize its histogram by running the next cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7124a3db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(binomial_population, stat=\"count\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1935bef1",
   "metadata": {},
   "source": [
    "The mean and standard deviation is not as straightforward as in the Gaussian case (since these parameters were needed to generate the data in that case). However you can easily compute those values by drawing them directly from the population:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "35e417f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian population has mean: 4.0 and std: 0.9\n"
     ]
    }
   ],
   "source": [
    "binomial_pop_mean = np.mean(binomial_population)\n",
    "binomial_pop_std = np.std(binomial_population)\n",
    "\n",
    "print(f\"Gaussian population has mean: {binomial_pop_mean:.1f} and std: {binomial_pop_std:.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c515c113",
   "metadata": {},
   "source": [
    "Once again, in real life you will not have access to the whole population so you need another method to compute this values. Actually the mean and standard deviation of binomal distributions are well defined and can be computed by using the following formulas:\n",
    "\n",
    "- $\\mu = np$\n",
    "\n",
    "\n",
    "- $\\sigma = \\sqrt{np(1-p)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bfeb5534",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian population has mean: 4.0 and std: 0.9\n"
     ]
    }
   ],
   "source": [
    "binomial_pop_mean = n * p\n",
    "binomial_pop_std = np.sqrt(n * p * (1 - p))\n",
    "\n",
    "print(f\"Gaussian population has mean: {binomial_pop_mean:.1f} and std: {binomial_pop_std:.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36ec734e",
   "metadata": {},
   "source": [
    "Now you have found these same values but without needing to sample the whole population. Nice!\n",
    "\n",
    "Before seeing the theorem for this case, you should know that there is a rule of thumb to know if the theorem will hold or not. This condition is the following:\n",
    "\n",
    "if $min(Np, N(1-p)) >= 5$ then CLT holds\n",
    "\n",
    "where $N = n*sample\\_size$\n",
    "\n",
    "However, it is important to note that this rule is only a rough guideline, and other factors such as the presence of outliers and the purpose of the analysis should also be taken into consideration when choosing an appropriate statistical method.\n",
    "\n",
    "Now check the theorem in action. Begin by using a small `sample_size`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5aca48fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The condition value is: 3.0. CLT should hold?: False\n"
     ]
    }
   ],
   "source": [
    "sample_size = 3\n",
    "N = n * sample_size\n",
    "\n",
    "condition_value = np.min([N * p, N * (1 - p)])\n",
    "print(f\"The condition value is: {condition_value:.1f}. CLT should hold?: {True if condition_value >= 5 else False}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f446cc20",
   "metadata": {},
   "source": [
    "Perform the sampling and compute the theoretical values for the mean and standard deviation of the sample means. Remember these latter two can be computed like so:\n",
    "\n",
    "- $\\mu_{\\bar{X}} = \\mu$\n",
    "\n",
    "\n",
    "- $\\sigma_{\\bar{X}} = \\frac{\\sigma}{\\sqrt{sample\\_size}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "43fbbd16",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute sample means\n",
    "binomial_sample_means = sample_means(binomial_population, sample_size=sample_size)\n",
    "\n",
    "# Compute estimated mu\n",
    "mu_sample_means = n * p\n",
    "\n",
    "# Compute estimated sigma\n",
    "sigma_sample_means = np.sqrt(n * p * (1 - p)) / np.sqrt(sample_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26c71c78",
   "metadata": {},
   "source": [
    "Visualize the KDE vs Gaussian curve plot and the QQ plot to see how well the theorem is holding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ced8cb91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the plots\n",
    "utils.plot_kde_and_qq(binomial_sample_means, mu_sample_means, sigma_sample_means)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e292d0cc",
   "metadata": {},
   "source": [
    "This doesn't look as good as with the Gaussian example. It looks that by using a small `sample_size` the sample means do not follow a Gaussian distribution.\n",
    "\n",
    "Try again but now increasing the size of each sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a15d5126",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The condition value is: 30.0. CLT should hold?: True\n"
     ]
    }
   ],
   "source": [
    "sample_size = 30\n",
    "N = n * sample_size\n",
    "\n",
    "condition_value = np.min([N * p, N * (1 - p)])\n",
    "print(f\"The condition value is: {condition_value:.1f}. CLT should hold?: {True if condition_value >= 5 else False}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "055109cb",
   "metadata": {},
   "source": [
    "According to the rule of thumb, the theorem should hold under these conditions. Run the next cell to check if this is true:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8b81b942",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "binomial_sample_means = sample_means(binomial_population, sample_size=sample_size)\n",
    "\n",
    "# Compute estimated mu\n",
    "mu_sample_means = n * p\n",
    "\n",
    "# Compute estimated sigma\n",
    "sigma_sample_means = np.sqrt(n * p * (1 - p)) / np.sqrt(sample_size)\n",
    "\n",
    "# Create the plots\n",
    "utils.plot_kde_and_qq(binomial_sample_means, mu_sample_means, sigma_sample_means)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a86335a",
   "metadata": {},
   "source": [
    "This time everything seems to indicate that the theorem is holding nicely!\n",
    "\n",
    "As with the previous distribution, by running the next cell you will launch an interactive widget in which you can play around with different values of $n$, $p$ and $sample\\_size$. \n",
    "\n",
    "See if you can find anything interesting, for instance does the theorem seem to hold better when $p$ is close to 0.5?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c292889c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a61f57a03e63415293612c309cd247a7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=2, continuous_update=False, description='n', max=50, min=2), FloatSlider…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.binomial_clt()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94932c33",
   "metadata": {},
   "source": [
    "Keep on going with another distribution!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bebe0789",
   "metadata": {},
   "source": [
    "## Poisson Population\n",
    "\n",
    "Another popular distribution you might have heard of is the `poisson` distribution. It models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence $\\mu$ of those events.\n",
    "\n",
    "Since you are already familiar with the process of checking the theorem for a distribution you will skip all intermediate steps and jump straight to playing with the interactive widget.\n",
    "\n",
    "The only thing to consider here is that the mean and standard deviation of this distribution can be computed like this:\n",
    "\n",
    "- $\\mu = \\mu$\n",
    "\n",
    "\n",
    "- $\\sigma = \\sqrt{\\mu}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ec6cf35c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9ecd32f9bbfa4cfeb508bc988267025b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.5, continuous_update=False, description='mu', max=5.0, min=0.01, rea…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.poisson_clt()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ccdb748",
   "metadata": {},
   "source": [
    "As expected, you should see that the bigger the `sample_size` the more closely the distribution of the sample means follows a Gaussian distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6152877c",
   "metadata": {},
   "source": [
    "## Cauchy Distributions\n",
    "\n",
    "The Cauchy distribution is not as well-known as the other ones seen throughout this lab. It has heavy tails, which means that the probability of observing extreme values is higher than in other distributions with similar spread. It also does not have a well-defined mean or variance, which makes it less suitable for many statistical applications.\n",
    "\n",
    "As a result of the properties of this distribution, the central limit theorem does not hold. Run the next cell to generate a population of 1000 points that distribute Cauchy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6b3b4880",
   "metadata": {},
   "outputs": [],
   "source": [
    "cauchy_population = np.random.standard_cauchy(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "493653bc",
   "metadata": {},
   "source": [
    "Now take a look at the histogram of this population:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fd66119d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(cauchy_population, stat=\"density\", label=\"hist\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7818e127",
   "metadata": {},
   "source": [
    "It is very difficult to even see the histogram due to the extreme values it has. Now compute the sample means with a `sample_size` of 30, which is usually a safe bet for the theorem to hold under other distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b58257ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "cauchy_sample_means = sample_means(cauchy_population, sample_size=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5477a70",
   "metadata": {},
   "source": [
    "Since this distribution has an undefined mean and standard deviation and the histogram is very hard to interpret you will only create the QQ plot for the sample means:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ee14767a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KkS4nTsCgQTBzprl9111Qtmw6L+ochQ8REREX++47ePpp58/Pnx86dIAWLVzwxNlr1+Cjj2DoUDh3ztzXtSu88475Rl6g8CEiIuJC8+ebz11xVO7cZiZwSeBI9vvvZovlr7/M7SpV4P334eGHXXBx5yl8iIiIuEhkJDzzjPPn1q/vokL++w/eeAO++MLczpMHRo+Gl17yzEIed6DwISIi4gLJa3g4o0gR5x/mlsK1a/Dhh2aLJS7O3PfiizBmjNdaLGlR+BAREXGB0aOdn1zqkpVF160zWyw7dpjbVauaLZbq1dN5YdfTImMiIiLpFBkJw4Y5fl5AgDlHJF13svz3H3TubE4U2bHDbLF89BFs2pQhgwcofIiIiKSL1WpOpXDGN9+Yz3lxyrVr8N57UKYMfPmluSBIt26wfz+8/HKGmNtxK2q7iIiIpEOHDnD6tGPnFCmSzrU71q6FXr2ut1iqVTNbLA895OQFPUvhQ0RExEnz5plf9urdG1q1SsettLGxMHAgfPWVuZ03r7m++gsvZOiRjpspfIiIiDhh/nxo397+40eMgLfecvLNrl2D6dPNiSXx8ddbLGPGQL58Tl7UexQ+REREHOToeh5588KQIU6+2Zo1Zovl77/N7QcfNFssDz7o5AW9TxNORUREHODMBNM+fZzoisTEwHPPQZ06ZvDIlw8+/hg2bvTp4AEKHyIiIg5p396xCaa5czs46nH1KkyZYj70bc4cs8XSvTvs22e2WrL4/o9utV1ERETs9Npr8O23jp3z2WcOjHqsWWMuFLZzp7n90ENmi6VaNcfeNIPz/fgkIiLiAQMGwOTJjp3z+ut2ruNx/Lh5z26dOmbwyJcPPvkENmzwu+ABGvkQERG5o/nzYdIk+4+3WMwFxNq2vcOBV6/CtGnmXSwXLlxvsbz9tjlL1U8pfIiIiNxGYqL5bDZHvPWWHcFj1SrzLpZdu8zt6tXNFkvVqs6U6VPUdhEREbmFyEjzYbDx8fafkzu3+VDZWzp+3Jy1Wq+eGTzCwuDTT2H9+kwRPEAjHyIiImmKjIQ2bRw/75YTTK9eNZ/FMnz49RbLK6/AqFF+3WJJi8KHiIjITaxW6NTJ8fMGDLjFBNOVK80Wy+7d5vbDD5stlipV0lWnr1LbRURE5AZWK9x/P1y86Nh5/fvDhAk37Tx2DNq1g8ceM4NHWBh8/jn8/numDR6g8CEiImITGWnO2UieA2qvJ5646W6Yq1dh4kQoVw7mzjUXBuvZ03zc/fPP+8VCYemhtouIiAjOz/EAs91i89tvZotlzx5zu0YNs8XywAPprtFfZO7oJSIigtlq6d3buXMLF4batYGjR+HZZ6F+fTN45M8PM2fCunUKHjdR+BARkUxv7VpzeoYz3puYSMCk8WaLZd48s6XSq5fZYunSJdO3WNKitouIiGR6MTGOn5MvHyzs9Su1h/eCvXvNnTVrmi2WypVdWp+/UfgQEZFMr0ABx45/+YmjfBDUnywj5ps77r4bxo+Hjh010mEHhQ8REcn0atc21/k6c+b2x2UjkU/KT6HzqlHmvbjJLZYRI+CuuzxSqz9Q+BAREcFccPR2GrCC2XleJXzPPnNHrVpmi+X++91fnJ/R2JCIiGR6a9fC6dNpv1aYI3zL06ygEeFn90F4OHzxhXmSgodTFD5ERCTTS2vCaTYSeYN32Es5nuY7rGRhX5M+sG+fufb6nYZK5JYUPkREJNO7ecJpQ5bzN5V4h8Hk5BJreYQH2EbMG1MhNNQrNfoThQ8REcn0kpdGL0I083mK5TSmLPuJJZyOfMmjrOFckfvMxcQk3TThVEREMq3ERChZEk4cTWAQk/kfb5OTS1wjgGm8ynCGE4850jF5MgQEeLlgP6GRDxERyZRefx0CA6HC0Z/5m0qM5U1ycok11OYBttGfKbbgAeYDacU1NPIhIiKZitVqrutxdEM039GPNkQCEEMEA5jI17QHUk8mdWYVVEmbRj5ERCTTiIyEu4ISqLthDHspRxsiuUYAk+lHWfbxNR1IK3iA46ugyq1p5ENERDKFyEj4uM1PbKU3ZfgHgNU8Sk/eZxcVb3vuXXehyaYupPAhIiJ+z3rgEFna9OMnFgFwnAIMYCLf0I5bjXTcaMYMTTZ1JbVdRETEf125Am+/TWLpCrRkEdcIYBL9KcdevrnF3I6bNWsGzzzj/lIzE418iIiIf1q2DKN3byz//ksQsJK69GI6u7nX7ktUrQpLlrivxMzKp0Y+1qxZQ7NmzShYsCAWi4VFixaleN0wDIYPH07BggUJCgqibt267Nq1yzvFioiIdxw6RFLzlvD441j+/ZfjFOBZvuExfnMoeDRrBlu2uK/MzMynwsfFixe5//77mT59epqvjx8/nsmTJzN9+nT++OMPIiIiaNiwIefPn/dwpSIi4klWK/wYeYX3C4ziconyZPl+MVfJygQGUJZ9zONZ7GmxJPv6a414uJNPtV2aNm1K06ZN03zNMAymTp3KkCFDaN26NQBffPEF4eHhfP3117z88sueLFVERDxkzhz45rmlTKUPj3MAgN+oRy+ms4cKDl/v22/h6addXaXcyKdGPm4nKiqK2NhYGjVqZNsXGBhInTp1WL9+/S3PS0hIID4+PsWXiIhkbImJ8M47UCogilzPteAHnqQUBzhGQdoyl/r86nDwCAyEBQsUPDzBb8JHbGwsAOHh4Sn2h4eH215Ly9ixYwkNDbV9FSlSxK11ioiI8xIT4dFHITTwMpcHj+DvpAq0YAlXycp4Xqcce/mWtjjSYgEoVAguXoT/HzgXN/Ob8JHMYkn5H5xhGKn23Wjw4MHExcXZvo4cOeLuEkVExEFWK7RqZY5O5F77AzupyAiGE8QVfuUx7ucv3mA8Fwhx+NoBAXD4sNbx8CSfmvNxOxEREYA5AlLghjVwT5w4kWo05EaBgYEEBga6vT4REXFOZCQ89RQUNw6ymL4053sAjlKI/kxmPk/j6EjHjebOVfDwNL8Z+ShRogQRERGsWLHCti8xMZHVq1dTs2ZNL1YmIiLO+uIL6NDmMm8Zw9lNBZrzPVfJyjgGUo69zOcZ0hM8Xn/dDDbiWT418nHhwgX+/fdf23ZUVBTbt28nb968FC1alL59+zJmzBhKly5N6dKlGTNmDMHBwbRv396LVYuIiKMuXIC8eaHx1e/ZRR/uIQqAX6jPq0xjL+XTdf0sWcwRD00u9Q6fCh9btmyhXr16tu3+/fsD0LlzZ2bNmsXAgQO5fPkyPXr04OzZs1SvXp3ly5cTEuJ4D1BERDwrMRHGj4e33jJbLAvoQzN+AOAIhenPZL7jKdIz0gHmSIdaLd5lMQzD8HYRGUl8fDyhoaHExcWRO3dub5cjIuL3EhPhscfg998hB5cZxDu8wThykEAi2ZhMf97mf1wkV7re57nn4LPPIHt2FxUuqdj7M9SnRj5ERMR/XLgAlSrBoUMABs34nnfpQwkOAbCCBrzKNPZRzqnr58gBNWvCwIHQoIFGOjIShQ8REfG4Bx6A7dvN39/DAd6jN0/wI2C2WPoxhQW0wZkWS8GCEBWlEY6MzG/udhERkYzt5EmIiACLxQweQVxiBG+xi3t5gh9JJBtjGUQ59rLAibkdxYvD+fNw7JiCR0ankQ8REXGrM2cgLAyuzzA0aM4S3qUPxTkMwM80ojfvsZ+yDl+/Vi347TcFDl+i8CEiIm4RFQX33JNyX0n+5T168zjLAIimCH2ZykJa4UyLJSFBocMXqe0iIiIulZhotlZuDB5BXGIkQ9nFvTzOMhLJxmjepDx7WEhrHA0exYqZIykKHr5JIx8iIuISyQ9927Tpxr0GLVjMVPraWiw/0ZjevMc/lHHqfc6dg9DQdJcrXqSRDxERSbfevc2Hvt0YPErxDz/yOItoRXEOc5iitCKSpixzKni88oo52qHg4fs08iEiIukSGgrx8de3g7nIm4xhABMJJJEEsjOB1xnDm1wm2OHrv/22+QwWtVj8h8KHiIg4zZJiqoZBKxYyhX4UIxqAZTShN+/xL6Udum62bOatuRrl8E8KHyIi4pQbg0dp9vMevWnCzwAcpih9eJfFtMCRyaQ5ckBsrEKHv1P4EBERhyUHj2AuMoTRvMYkW4tlPAMZy2CHWyznz0Ou9D2+RXyEwoeIiDjEfEaKQWsimUI/inIEgB9pSm/e4wCl7L5WjhzmeiAREe6pVTImhQ8REbGbxQJl2Mc0XqURKwA4RDH68C5LaI69LZbwcIiO1iTSzEq32oqIiF1yWi4yhsH8TSUasYIrBDKSoVRgN0vsnNvRsKHZXomNVfDIzDTyISIit2cYPJVlAXvpRxGOArCUx+nNexykpCOXEQE08iEiIrdxZv1eVmRpxHc8TRGOEkVxmrOYJ/nB7uBx9KiCh6Sk8CEiIqlduMDk7IPIVes+GvILVwhkBG9Rgd1878DcDsOAQoXcW6r4HrVdRETkOsPA+u13HH+2P/3/v8XyPU/Sl6kOtVj+/1IiadLIh4iImPbs4ViFhgQ8+wxFOMpBStCMJTTnewUPcSmFDxGRzO7CBXjjDa5WuI9Ce3/lMjkYxnDuZRc/0Mzhyyl4yJ2o7SIiklkZBsyfD/37w7FjZAOW0Iy+TCWKe5y+pMidKHyIiGRGe/ZAr17w228AHOAe+vAuS3nS6UsqeIi91HYREclMzp83n09/333w229cJgdvMYJ72eV08KhYUcFDHKORDxGRzMAwYN48eO01OH4cgFWhzXk+biqHKOH0Zb/+Gtq1c1WRklkofIiI+Ltdu+DVV2HlSnP7nnu4PO496j39RLoue+1a8kPmRByjtouIiL86fx4GDIDKlc3gkSMHjBwJu3YRnM7gYRgKHuI8jXyIiPgbw4C5c83g8f8tFlq2hClToHhxcuRw/tKHD0PRoi6pUjIxhQ8REX+ya5d5F8uqVeZ2yZIwbRo0bQrAmTOQkODcpTWpVFxFbRcREX8QH29OJr3/fjN4BAXBqFGwc6cteADky+fc5RU8xJU08iEi4ssMw7zl5PXXISbG3NeqldliKVYsxaEW+54Fl+ZbiLiSwoeIiK/auRN69oQ1a8ztUqXMFkuTJqkODQ527i2uXUtHfSK3oLaLiIiviY83l0SvXNkMHkFB8PbbZhhJI3icOQOXLzv+Nl9+qTtaxD008iEi4isMA+bMMVsssbHmvtatYfLkVC2WGzkzzyN3bujY0ck6Re5A4UNExBf8/bfZYlm71twuXdpssTRufNvT9u1z7u3OnHHuPBF7qO0iIpKRxcVBv37wwANm8AgOhjFjzDByh+ABUK6c42+pdou4m0Y+REQyIsOA2bPNFst//5n72rQxWyx2rvLlzOhF/vxqt4j7KXyIiGQ0O3aYLZZ168ztMmXMFkujRg5dpmZNx9/6xAnHzxFxlNouIiIZRVwc9OkDVaqYwSM4GMaONcOIg8EDHJ/vofU8xFM08iEi4m2GAV99BQMHXm+xPPWU2WIpUsSpSyYmOnZ8u3ZOvY2IUxQ+RES86a+/zBbL77+b22XLmi2Whg3TddlcuRw7/rPP0vV2Ig5R20VExBvOnYPevc0Wy++/Q86cMG6c2WJJZ/A4cwauXnXsnKCgdL2liEM08iEi4klJSddbLMmzO595BiZNgsKFXfIWji4q5uzD5kScpfAhIuIp27ebLZb1683tcuXMFkuDBi57C2ceHrdzp8veXsQuaruIiLjbuXPw6qtQtaoZPHLmhPHjzfkeLgoeu3c7/9TaiAiXlCBiN418iIi4S1ISfPEFvPEGnDxp7mvbFiZOdFmLBZwPHQAHD7qsDBG7aeRDRMQdtm2DRx6Brl3N4FG+PPzyC8yd65Lgcfky1K2bvuABUKJEuksRcZjCh4iIK509a87rqFYNNmwwWywTJpjzPerXT/flt241A0dwMKxenb5rHT2a7nJEnKLwISLiCklJ8Pnn5lLoH3xgbj/7rLnM6IABkD17ui7/ySdm6KhWzTXlZssGhQq55loijtKcDxGR9PrzT3O0Y+NGc7tCBZg+HerVc/qSGzY492wWezm6AqqIKyl8iIg468wZ+N//4KOPzCXSc+WC4cPNxcOyZXPoUseOuXQO6m3pGS7ibQofIiKOSkqCmTNh0CA4dcrc166deRdLwYJ2XSIuDooWhfh4N9aZBgUPyQgUPkREHLF1q9li2bTJ3L73XrPFUrfubU/z5MjGrSh4SEahCaciIvY4cwZeeQUefNAMHiEh5pLo27alGTyWLDEniCZ/KXiIXKeRDxGR20m+i2XQIDh92tzXvr15++z/t1guXzYXL92zx4t13sKOHVCpkrerEElJ4UNE5Fa2bDFbLJs3m9sVK2J9dzotJtdhqQ/cpqrRDsmo1HYREbnZ6dPQvTvGQw/B5s3EE0JfppBt559krV+HpUu9XeCtWSywa5eCh2RsCh8iIsDgwZDFkkQ3yyecDisDM2ZgMQy+4jnKso936cs1HLt91pNmzzYDR1KSucyISEamtouIZCrvvgt9+6beX40/2EhPHuIPAHZQiV5MZy2PerZAB61fDzVqeLsKEcdo5ENE/NILL6S82yT56+bgkZfTfMTLbKI6D/EHceSmD1Opwp8ZNnj07QvXrpkjHQoe4os08iEiPmvaNHMxUWdkwcqLfMoY3iQfZwD4ko4MZDz/EeHCKl1j1SqoU8fbVYi4hsKHiGR4t2qVOOtBNvM+PXmQLYDZYunJ+6yjtuveJJ0+/dQcvRHxR2q7iEiGYW+rxFn5OMXHdGMjD/MgW4gjN715lyr86fXgMXmy2UZJ/lLwEH/ml+Hjgw8+oESJEuTIkYOqVauydu1ab5ckIv/vs8/SDhgWi7mWlztkwcrLfMR+ytCNT8mCwRd0oiz7mEZvrF4YBH7vvZRho18/j5cg4jV+Fz7mzZtH3759GTJkCNu2baN27do0bdqU6Ohob5cmkql88knaAePFFz1bx0NsYhPV+YhXyMtZtnM/tVhHF77w6NyOxYtTho1XX/XYW4tkOH4XPiZPnswLL7zAiy++SPny5Zk6dSpFihThww8/9HZpIn5rwoTUIeOll7xbUxgn+YQX2cTDVGMr5wjlVd6jGltYTy23vvfAgSmDhmFA8+ZufUsRn+JXE04TExPZunUrgwYNSrG/UaNGrF+/Ps1zEhISSEhIsG3He/r51iI+ZsMGqFnT21XcWhasvMTHjGYIeTkLwCw68wbjOEG4y9+vd29zQqyI2M+vRj5OnTqF1WolPDzlXzDh4eHExsamec7YsWMJDQ21fRUpUsQTpYr4jBUrUo5oZOTgUZ2NbOYhPqQHeTnLNipTk995nlkuCR7Dh6ce0VDwEHGcX4WPZBaLJcW2YRip9iUbPHgwcXFxtq8jR454okSRDOvyZShb9nrYaNTI2xXdWRgn+ZQX2EgNqvIn5wilF9N4kD/YgHNpae/e1EFj2DAXFy6SSflV+AgLCyMgICDVKMeJEydSjYYkCwwMJHfu3Cm+RDKj5HkbwcGwf7+3q7FPFqy8wgfspwwvYN4q8znPU4b9vE8vu+5iiYxMHTIMwwxgIuIefjXnI3v27FStWpUVK1bQqlUr2/4VK1bQokULL1YmkjEdOwaFC3u7Cuc8zAbepydV2AbANirTgw/YSOr1xkNC4NAhyJvXw0WKSJr8auQDoH///nz66ad8/vnn7Nmzh379+hEdHU337t29XZpIhnHsmDnK4YvBIz8n+IyubKAmVdjGWe6iB+9TjS30+LJGmqMY8fEKHiIZiV+NfAC0bduW06dPM3LkSGJiYqhYsSI//vgjxYoV83ZpIhlCtmzmQ8l8TRasdOcj3uZ/5OGcubNrV/KMHcsHd9/NB16tTkQcYTEMw/B2ERlJfHw8oaGhxMXFaf6H+JULF8z2g6/Inh0OH4aICMznxvfsCdu3my8+8AC8/74e6SqSwdj7M9Tv2i4iktr992fc4PHpp2lP+ExIgAjLf9ClC9SqZQaPu+6CDz6AP/5Q8BDxYX7XdhGRlG5xl7nHzZ4NHTrYefC1a/DhhzB0KMTFmfteeAHGjoX8+d1Wo4h4hsKHiB/zVvBYuxYeecTJk3//3Wyx/PWXuV2litliefhhl9UnIt6ltouIn/JU8Jg4MXXLxKng8d9/0LmzefJff0GePObox+bNCh4ifkYjHyJ+yJ3B4+OPoVs3F17w2jVzHsfQoeY9sRbL9RZLWJgL30hEMgqFDxE/YrVCVhf/Xz1wIIwb59pr2qxdC716wY4d5na1amaL5aGH3PSGIpIRqO0i4iciI10XPAIC4OBBs4XiluARGwudOsGjj5rBI29e+Ogj2LhRwUMkE1D4EPEDM2dCmzbpv8748WbguHYNSpRI//VSuXYNpk41H5zy1Vdmi6VbN9i3D15+2Uw9IuL31HYR8XGhoeZUifRy+3KDa9aYLZa//za3q1Uz53o8+KCb31hEMhqNfIj4sLvuSn/w2LLFzcEjJgY6doQ6dczgkTcvzJhhtlgUPEQyJY18iPiokyevr7/lLLeGjqtXYfp0GDYMzp83WywvvQSjR0O+fG58YxHJ6BQ+RHzU3Xen73y3Bo81a8yFwnbuNLcffNBssVSr5sY3FRFfobaLiA9K7zoebgseMTHw3HNmi2XnTnOE45NPzBaLgoeI/D+FDxEfU7p0+s53S/C4ehUmTzbvYpkzx0xH3bubd7G8+CJk0V81InKd2i4iPuTCBfj3X+fPd0vwWLXKvItl1y5z+6GHzIXCNNIhIregf46I+JCQEOfOu+suNwSP48ehfXuoV88MHvnywaefwoYNCh4iclsKHyI+Yt8+584LD4ezZ11YyNWrMGmS2WL55huzxfLKK7B/v/lMFrVYROQO1HYR8RHlyjl+zqpV5txPl1m50myx7N5tblevbrZYqlZ14ZuIiL/TP1FEfMDQoc6d57LgcewYtGsHjz1mBo+wMPjsM1i/XsFDRBym8CGSwVmt8Pbbjp/nkjkeV6/CxInmsMvcuWZLpWdPs8XStataLCLiFLVdRDI4Z55Ue/SoC974t9/MFsuePeZ2jRpmi+WBB1xwcRHJzPTPFpEMzNnFxAoVSsebHjsGzz4L9eubwSN/fvj8c1i3TsFDRFxC4UMkgypa1LnzTp928g0TE2H8ePMulnnzzJZKr17mbTbPP68Wi4i4jMMDukeOHMFisVC4cGEANm/ezNdff02FChV46aWXXF6gSGYUFwdHjjh+Xr585kNjHfbrr2bQ2LvX3K5Z02yxVK7sxMVERG7P4X/KtG/fnpUrVwIQGxtLw4YN2bx5M2+++SYjR450eYEimdFddzl33qlTDp5w9Ci0bQsNGpjBI39+mDkT1q5V8BARt3E4fOzcuZOHHnoIgG+//ZaKFSuyfv16vv76a2bNmuXq+kQyldhY5+d5xMQ4cHBiIowbZ97F8u23Zkvl1VfNu1i6dFGLRUTcyuG2y9WrVwkMDATgl19+oXnz5gCUK1eOGIf+9hORG+XMCZcuOXduYCBERNh58C+/XJ/LAVCrFkyfrpEOEfEYh/95c++99/LRRx+xdu1aVqxYQZMmTQA4fvw4+fLlc3mBIplBeoIHwJUrdhx05Ag8/TQ0bGgGj7vvhi++UItFRDzO4fAxbtw4ZsyYQd26dWnXrh33338/AEuWLLG1Y0TEfrGx6Qsed1xMLDER3nnHbLF8953ZUund2wwgnTo53+cREXGSxTAcXwfRarUSHx9Pnjx5bPsOHTpEcHAwd999t0sL9LT4+HhCQ0OJi4sjd+7c3i5HMoH0/Ow/ccKcI3pLy5dfn8sB8MgjZovl///RICLiSvb+DHVqVplhGGzdupUZM2Zw/vx5ALJnz05wcLBz1YpkUukJHiEhtwke0dHw1FPQuLEZPMLD4csvYc0aBQ8R8TqHJ5wePnyYJk2aEB0dTUJCAg0bNiQkJITx48dz5coVPvroI3fUKeJ30tvtiI9PY2dCAkyebD4M5tIlCAgwJ5eOGAGhoel7QxERF3F45KNPnz5Uq1aNs2fPEhQUZNvfqlUrfv31V5cWJ+Kv0hs80myW/vwzVKoEb75pBo9HHoE//4SpUxU8RCRDcXjkY926dfz+++9kz549xf5ixYpx7NgxlxUm4q8++cT5c7NkMZ9ym0J0NPTrB5GR5nZEBEyYAB06aDKpiGRIDo98JCUlYU31tx8cPXqUkJAQlxQl4q+sVnD2KQSzZt0UPBISYMwY8y6WyEizxdKvn3kXy3PPKXiISIblcPho2LAhU6dOtW1bLBYuXLjAsGHDePzxx11Zm4jf+f/1+Rx27hx07nzDjp9+MlssQ4bA5cvw6KOwbZs530N3aYlIBudw22XKlCnUq1ePChUqcOXKFdq3b88///xDWFgY33zzjTtqFPELZ86k0TKxw/333zBl4/Bhc3Rj4UJzOyICJk6E9u010iEiPsOpdT4uX77MN998w59//klSUhJVqlShQ4cOKSag+iqt8yHu4mw2MAzMJUwnTjTbLJcvmy2WPn1g2DCNdIhIhmHvz1Cnwoc/U/gQd9i9G+691/HzDANYtsxckfTff82ddeqYC4VVrOjSGkVE0sven6EOt12+/PLL277eqVMnRy8p4vecCh5Rh6BlX1i82NxRoIA5+tGunVosIuLTHB75uHFJdTCfcnvp0iXbCqdnzpxxaYGeppEPcTVHc0IgVzgxYAK5p48x2y0BAdC3L7z1llosIpKhuW3k4+zZs6n2/fPPP7zyyiu8/vrrjl5OxK/NnOnY8U35kffoTe6JB8wddeuaLRZnhk5ERDIol8352LJlC8899xx79+51xeW8RiMf4ipWK2S1M94XJ4qp9KUFS8wdBQvCpEnQtq1aLCLiM9z6YLm0BAQEcPz4cVddTsTn2fOcxUCuMJSR7KYCLVjCVbLCgAGwdy88+6yCh4j4JYfbLkuWLEmxbRgGMTExTJ8+nVq1armsMBFfduYMJCbe/pgn+IF36UNJDgLwG/Wos2M6VKrggQpFRLzH4fDRsmXLFNsWi4X8+fPz2GOPMWnSJFfVJeLTbvmoe6AEB5lKX5rzPQDHKEh/JtPks2cIqKSRDhHxfw6Hj6SkJHfUIeI34uIgrf9NcnCZgYxnMGPJQQJXycoU+jGKoVzLEcK8rp6vVUTEGxwOHyJye2XKpN73JN/zLn24hygAfqE+rzKNvZQHwLjsyQpFRLzLrvDRv39/uy84efJkp4sR8XWJiXDixPXtEhzkXfrQjB8AOEoh+jGF73gKMFssR496oVARES+yK3xs27bNrotZNDNfMrl33jF/zcFl3mAcg3jH1mKZxGu8zf+4SC7b8RYLFCrkpWJFRLxEz3a5idb5kPQIymHQMOF7ptLX1mJZQQNeZRr7KJfq+EuXwA+exygiArhxhVMRuYUDB/guoTdP8CMARyhMP6awgDYkt1hupuAhIpmRU+Hjjz/+YP78+URHR5N402IGkZGRLilMxGdcumT2W8aP5wkSSCQbk3iN0QxJ0WK52cGDHqxRRCQDcXiF07lz51KrVi12797NwoULuXr1Krt37+a3334jNDTUHTWKZEyGYT5x9t57YdQoSEhgOQ2pxN+8ydjbBg+AEiU8VKeISAbjcPgYM2YMU6ZM4YcffiB79uy8++677Nmzh2eeeYaiRYu6o0aRjOfff+GJJ6BlSzh0CIoU4c83v6MxP7Ofsnc8fcgQt1coIpJhORw+Dhw4wBNPPAFAYGAgFy9exGKx0K9fPz7++GOXFyiSoVy6BEOHmqMdy5ZBtmwweDDs2UO3n249t+NmcXHuLVNEJCNzOHzkzZuX8+fPA1CoUCF27twJwLlz57h06ZJrqxPJKAwDFi2CChXg7bfNBT0aNYK//4YxYyBnTg4dsv9yJUu6q1ARkYzP4fBRu3ZtVqxYAcAzzzxDnz596NatG+3ataN+/fouL1DE6/75Bx5/HFq1gsOHoWhRWLAAfvoJyl5vseTMaf8le/RwQ50iIj7C7rtdtm/fTuXKlZk+fTpXrlwBYPDgwWTLlo1169bRunVrhg4d6rZCRTzu0iVzVGPCBHOkI3t283H3b76ZZtK4cMG+ywYGmpcSEcms7F5kLEuWLDzwwAO8+OKLtG/f3m/vbNEiY4JhwMKF0K8fREeb+xo3hvfeS/vBLf/PkQV+tbSfiPgje3+G2t12+f3336lSpQqDBg2iQIECPPfcc6xcudIlxYpkGPv3Q9Om0KaNGTyKFoXISHNy6W2Ch4iI2M/u8FGjRg0++eQTYmNj+fDDDzl69CgNGjSgZMmSjB49mqN6Opb4sosXzXZKpUrw889mX2TIENizx5zrcYdhjcsOPJU2R4501ioi4uMcnnAaFBRE586dWbVqFfv376ddu3bMmDGDEiVK8Pjjj7ujRhH3MQxz8mj58jB2rDm3o2lT2LnTvKslONiuyzgygfSxx5ysVUTETzgcPm5UsmRJBg0axJAhQ8idOzc///yzq+pKZfTo0dSsWZPg4GDuuuuuNI+Jjo6mWbNm5MyZk7CwMHr37p1q+XcRm/37oUkTeOopOHIEihUzb6dduhRKl3boUnPm2H+sbgoTkczO6QfLrV69ms8//5wFCxYQEBDAM888wwsvvODK2lJITEzk6aefpkaNGnz22WepXrdarTzxxBPkz5+fdevWcfr0aTp37oxhGEybNs1tdYkPunjRHNWYNAmuXjVbLG+8AYMG2T3ScbOrV+0/tlcvp95CRMRvOBQ+jhw5wqxZs5g1axZRUVHUrFmTadOm8cwzz5DTkUUOnDBixAgAZs2alebry5cvZ/fu3Rw5coSCBQsCMGnSJLp06cLo0aN154pcb7H06wfJc5QefxzefRdKlfJYGbrNVkQyO7vDR8OGDVm5ciX58+enU6dOdO3albJl7/wMC0/ZsGEDFStWtAUPgMaNG5OQkMDWrVupV69emuclJCSQkJBg246Pj3d7reIFe/fCq6/CL7+Y28WLm6GjWTPH7pFNJzdndBERn2B3+AgKCmLBggU8+eSTBAQEuLMmp8TGxhIeHp5iX548eciePTuxsbG3PG/s2LG2URXxQxcumC2WyZPN3khg4PUWS1CQS97CkWlFt5iuJCKSqdg94XTJkiW0aNHCpcFj+PDhWCyW235t2bLF7utZ0vgXrGEYae5PNnjwYOLi4mxfR44cceqzSAZjGDB/vnkXy7hxZvB44gnYtQtGjHBZ8ABz7TF7OTmlRETErzg94dQVevXqxbPPPnvbY4oXL27XtSIiIti0aVOKfWfPnuXq1aupRkRuFBgYSGBgoF3vIT5i715zVuevv5rbxYubCaFZM7e83aJF9h+r22xFRLwcPsLCwggLC3PJtWrUqMHo0aOJiYmhQIECgDkJNTAwkKpVq7rkPSSDu3ABRo2CKVOut1gGDTLbLC4c6bjZuXP2HztlitvKEBHxGV4NH46Ijo7mzJkzREdHY7Va2b59OwClSpUiV65cNGrUiAoVKtCxY0cmTJjAmTNnGDBgAN26ddOdLv4uucXSvz8cO2bua9YMpk6Fe+5x+9vbe/dK7txuzUAiIj7DZ8LHW2+9xRdffGHbfuCBBwBYuXIldevWJSAggKVLl9KjRw9q1apFUFAQ7du3Z+LEid4qWTxhzx6zxfLbb+Z2iRJmi+XJJz1WQqFCsG3bnY979FH31yIi4gvsCh9Lliyx+4LNmzd3upjbSV5f5HaKFi3KDz/84Jb3lwzm/HkYOdIc3bh2zXxgyqBBMHCgx4cX7H1CrZ5kKyJisit8tGzZMsW2xWLBuOFv0hvvJrFara6pTCQthgHz5sFrr8Hx4+a+5s3NEFKihFdKiopy7XEiIv7Orlttk5KSbF/Lly+ncuXKLFu2jHPnzhEXF8ePP/5IlSpV+Omnn9xdr2Rmu3ebD0Zp184MHvfcAz/8AIsXey14gP1LqzuyBLuIiD9zeM5H3759+eijj3jkkUds+xo3bkxwcDAvvfQSe/bscWmBIpw/b67N8e6711ssgwebLZYM8Hz6bNlce5yIiL9zOHwcOHCA0NDQVPtDQ0M5dOiQK2oSMRkGzJ0LAwZcb7G0aGHer+rFkY6bJSXZd5yL7ioXEfF5dq9wmuzBBx+kb9++xMTE2PbFxsby2muv8dBDD7m0OMnEdu0yV+Rq394MHiVLmo+6X7QoQwUPq9Vc08wef//t3lpERHyFw+Hj888/58SJExQrVoxSpUpRqlQpihYtSkxMTJqPuhdxSHy8OZn0/vth1SrzzpVRo2DnTvMJtBlM8h2+9rB3hERExN853HYpVaoUO3bsYMWKFezduxfDMKhQoQINGjS47TNURG7LMOCbb8wWS/KoWsuWZovFziX2veGrr+w/tkgR99UhIuJLnFpkzGKx0KhRIx599FECAwMVOiR9du40FwpbvdrcLlXKXCisaVPv1mWHs2ftPzb544mIZHYOt12SkpIYNWoUhQoVIleuXET9/+IFQ4cOVdtFHBMfby6JXrmy+ZM5KAjeftucHOEDwQPgwAH7jgsIgLx53VuLiIivcDh8vP3228yaNYvx48eT/YaHWlSqVIlPP/3UpcWJnzIMmDMHypY12ypWK7RqZS6VPmRIhrh91l6nT9t3XL587q1DRMSXOBw+vvzySz7++GM6dOhAQECAbf99993HXnun/Uvm9fffULcuPPccxMaaLZZlyyAyEooV83Z1DrO346jOpIjIdQ6Hj2PHjlGqVKlU+5OSkriqJRzlVuLioF8/eOABWLPGbLGMHm3O92jSxNvVOS083LXHiYhkBg6Hj3vvvZe1a9em2j9//nzbk2ZFbAwDZs82WyxTp5otljZtzMUx3nwTAgO9XWG6BAe79jgRkczA4btdhg0bRseOHTl27BhJSUlERkayb98+vvzySz1RVlLascO8iyU5rJYpA9OmQaNG3q3Lha5cce1xIiKZgcMjH82aNWPevHn8+OOPWCwW3nrrLfbs2cP3339Pw4YN3VGj+Jq4OOjTB6pUMYNHcDCMGWOGET8KHgBnzrj2OBGRzMChkY9r164xevRounbtymotWiA3Mwxz1a2BA+G//8x9Tz0FkyZB0aLerc1N7O0a+Xh3SUTEpRwa+ciaNSsTJkzAarW6qx7xVX/9BbVrQ+fOZvAoUwaWL4f58/02eID9i68+9phbyxAR8SkOt10aNGjAqlWr3FCK+KRz56B3b7PF8vvvZotl7FizxeLnbTir1bxxxx7jxrm3FhERX+LwhNOmTZsyePBgdu7cSdWqVcmZM2eK15s3b+6y4iQDS0q63mI5ccLc9/TTZoslkzzE5LffICHBvmNnzoS+fd1ajoiIz3A4fLzyyisATJ48OdVrFotFLZnMYPt26NkT1q83t8uWhenToUEDr5blabNm2X+svcuwi4hkBk492+VWXwoefu7cOXj1Vaha1QweOXOa/YQdOzJd8ADzY9urZEn31SEi4muceqptsitXrpDDh57DIU5KSoIvvzRbLCdPmvueecZssRQu7N3avMgw7D+2Rw/31SEi4mscHvmwWq0pnmp78OBBQE+19VvbtsEjj8Dzz5vBo1w5+OUXmDcvUwcPgEqV7DuuXDm44RmMIiKZnsPhY/To0XqqbWZw9qy5Omm1arBhg9liGT/evKW2fn1vV5chPPecfcdNnOjeOkREfI2eaispJSXB55+bk0jff9/cbtvWfBbL66/rn/A3+Ptv1x4nIpJZ6Km2ct2ff0KtWvDCC2aLpXx5+PVXmDs307dY0jJ7tmuPExHJLPRUWzFbLD17mi2WjRshVy6zV/DXX1qa8zaSV5B31XEiIpmFnmqbmSUlmatfDRoEp06Z+9q1gwkToFAh79bmA4KDXXuciEhmoafaZlZbt0LNmvDii2bwqFDBXLLz668VPOx0zz2uPU5EJLNwap2Pxo0b07hxY1fXIp5w5gwMGQIzZpgLVeTKBSNGmIuHZcvm7ep8yg3zrV1ynIhIZpGuRcbEhyTfxTJoEJw+be5r395ssRQs6N3afFRcnH3Hqe0iIpKSXeEjT548WCwWuy545syZdBUkbrBlizmhdPNmc/vee81nsdSt69WyfJnVaq6/Zg9HVkIVEckM7AofU6dOtf3+9OnTvP322zRu3JgaNWoAsGHDBn7++WeGDh3qliLFSadPmy2Wjz82fwKGhJgtll691GJJp1WrzABijywOz6wSEfFvdoWPzp07237fpk0bRo4cSa9evWz7evfuzfTp0/nll1/o16+f66sUxyQlwWefweDB11ssHTqYLZYCBbxbm5/47Tf7j82d2311iIj4Iof/Tfbzzz/TpEmTVPsbN27ML7/84pKiJB3++AMefhheeskMHhUrmv9Mnz1bwcOFDh+2/9iOHd1Xh4iIL3I4fOTLl4+FCxem2r9o0SLy5cvnkqLECadPw8svQ/XqZgAJCYEpU8xVS+vU8XZ1fsfeeRxZs+pROCIiN3P4bpcRI0bwwgsvsGrVKtucj40bN/LTTz/pwXLeYLXCp5/Cm2+at9GC+cSz8eM10uFGERH2Hde0qW61FRG5mcPho0uXLpQvX5733nuPyMhIDMOgQoUK/P7771SvXt0dNcqtbN5s3sWyZYu5XamS+TC42rW9W1cm8Pnn9h33zz/urUNExBc5FD6uXr3KSy+9xNChQ5kzZ467apI7OXXKHOn49FNz/D93bhg50gwiWbV0i7slJsK5c/Yde/CgW0sREfFJDs35yJYtW5rzPcRDrFb46CPzcfeffGIGj44dYd8+6NNHwcNDpkyx/9jERPfVISLiqxyecNqqVSsWLVrkhlLktjZtMieTvvKKObfjvvtg7Vr48kv7JyCIS/zvf96uQETEtzn8T+VSpUoxatQo1q9fT9WqVcmZM2eK13v37u2y4gQ4edJcr+Ozz8zt3Lnh7bfNEKKRDo+7cAGuXbP/+HLl3FeLiIivshiGY4s/lyhR4tYXs1g46ONN7vj4eEJDQ4mLiyO3N1eHslrNlUmHDIGzZ819nTvDuHEQHu69ujI5O58yYHP6NOTN655aREQyGnt/hjr8T+eoqKh0FSZ22LjRnDz655/m9v33m3ex1Krl3boyOUeDByh4iIikxemnTpw6dYrTyUt3i2ucPAkvvAA1apjBIzQUpk0zb6VV8PAqZ4LH4MGur0NExB84FD7OnTtHz549CQsLIzw8nLvvvpuwsDB69erFOXvvPZTUrFb44AMoU+b6AhJduph3sfTqpbkdXuZM8AAYPtylZYiI+A27f6qdOXOGGjVqcOzYMTp06ED58uUxDIM9e/Ywa9Ysfv31V9avX0+ePHncWa//2bDBbLEkP5+9cmWzxVKzplfLEvOmImefGFCsGGTP7tp6RET8hd3hY+TIkWTPnp0DBw4QftOEx5EjR9KoUSNGjhzJFEcWQcjMTpyAQYNg5kxzOzQURo+G7t21HreXWa3mXI34eOevsXOn6+oREfE3drddFi1axMSJE1MFD4CIiAjGjx+vBcjsYbWaIxtly14PHs8/D/v3myMgCh5ek5gILVuaXa70BI/774dcuVxWloiI37F75CMmJoZ77733lq9XrFiR2NhYlxTlt9avNwPG9u3m9gMPmEHk/x/QJ95htUKzZrBsmWuul/zHKyIiabN75CMsLIxDhw7d8vWoqCjyOdsg93cnTpijG7VqmT+Z7rrLDB1//KHg4UUXLpijFFmzui54OLZqjohI5mR3+GjSpAlDhgwhMY2HVSQkJDB06FCaNGni0uL8wuLF5l0ss2aZ2127mi2WHj3UYvGCxERzeXSLBUJCYMcO111bwUNExD52t11GjBhBtWrVKF26ND179qTc/68bvXv3bj744AMSEhL46quv3FaozypdGi5ehCpVzNGOhx/2dkWZ0rFj5h0oVqt7rq/gISJiP4eWV4+KiqJHjx4sX76c5NMsFgsNGzZk+vTplCpVym2FeopbllffsAEeekgjHR528qT5/D13T0VS8BARMdn7M9ThZ7sAnD17ln/++QcwHzSX14/WkM4wz3YRpyQmwjvvwLBhnnk/BQ8Rkevc9mwXgDx58vDQQw85XZyIq124YI5yeOrRQ59+aq6ELyIijtO63eKzrFZzPm/bto495j69rl1TB01EJD2cfrCciDd98YV5i2ybNp4LHjExZptFwUNEJH008iE+JzQ0fSuQOuqff8AP5lKLiGQYCh/iMxITITDQc+93+DAULeq59xMRySzUdhGf8NprngseBw+a7RUFDxER99DIh2R4Dz1krkTvToULw59/Qv787n0fERFR+JAMrn9/9wWP/PnN5dUjItxzfRERSZtPtF0OHTrECy+8QIkSJQgKCqJkyZIMGzYs1XNmoqOjadasGTlz5iQsLIzevXun+Swa8Q1xcTBlimuvGRwMR4+abZUTJxQ8RES8wSdGPvbu3UtSUhIzZsygVKlS7Ny5k27dunHx4kUmTpwIgNVq5YknniB//vysW7eO06dP07lzZwzDYNq0aV7+BOKoJ5+EpUtdd70FC6BFC90mKyKSETi1vHpGMGHCBD788EMOHjwIwLJly3jyySc5cuQIBQsWBGDu3Ll06dKFEydO2L1UupZX9z5X3UobGmresRIamv5riYjIndn7M9Qn2i5piYuLS/FMmQ0bNlCxYkVb8ABo3LgxCQkJbN269ZbXSUhIID4+PsWXeIfVai4clt4/gq5d4dIlOHdOwUNEJCPyyfBx4MABpk2bRvfu3W37YmNjCQ8PT3Fcnjx5yJ49O7G3eazp2LFjCQ0NtX0VKVLEbXXLrUVGmsEjPY+8P3fOnMvx2WcQFOSy0kRExMW8Gj6GDx+OxWK57deWLVtSnHP8+HGaNGnC008/zYsvvpjiNYvFkuo9DMNIc3+ywYMHExcXZ/s6cuSIaz6c2C0y0lwm3VnZspmhQ6McIiK+wasTTnv16sWzzz5722OKFy9u+/3x48epV68eNWrU4OOPP05xXEREBJs2bUqx7+zZs1y9ejXViMiNAgMDCfTkspmSgtUKHTo4f37OnOYTbUVExHd4NXyEhYURFhZm17HHjh2jXr16VK1alZkzZ5IlS8pBmxo1ajB69GhiYmIoUKAAAMuXLycwMJCqVau6vHZxjVGj4MoV58+Pi3NdLSIi4hk+cbfL8ePHqVOnDkWLFuXLL78k4Ib7JSP+f6EGq9VK5cqVCQ8PZ8KECZw5c4YuXbrQsmVLh2611d0unmO1mkumOzvPY8ECaN3atTWJiIjz7P0Z6hPrfCxfvpx///2Xf//9l8KFC6d4LTk7BQQEsHTpUnr06EGtWrUICgqiffv2tnVAJOMZMULBQ0QkM/KJkQ9P0siHZzg76vHmmzBypBYLExHJiPxq5EP8z2+/ORY8smSBxESFDhERf+CT63yI73O0ZaLgISLiPxQ+xOOaNXPs9tihQxU8RET8icKHeNS8efDDD/YfnzUrDBvmvnpERMTzFD7EY6xWeP55x86ZM0ejHiIi/kbhQzxm1Sq4fNn+44sXh2eecVc1IiLiLQof4jEffODY8bt3u6cOERHxLoUP8QirFZYts//4GjX0ZFoREX+l8CEesXat/S0Xi8U8XkRE/JPCh3jEsWP2H/vWW5pkKiLizxQ+xCNOnrTvuOzZzXU9RETEfyl8iEcsX27fca+8olEPERF/p/Ahbteihf2TTZs1c28tIiLifQof4lYDBsCSJd6uQkREMhKFD3GbxESYNMmxc06ccE8tIiKScSh8iNtUqeL4OQUKuL4OERHJWBQ+xOWsVmjTBnbtcuy8/Pmhdm331CQiIhmHwoe4VGQk5Mxp/uqoDz7QnS4iIplBVm8XIP4jMtIc8XBG//7w1FOurUdERDImjXyIS1it8OKLzp3bvLnjE1NFRMR3KXyIS6xaBWfPOn5e376weLGrqxERkYxM4UNcYtUqx89p0wamTHF5KSIiksEpfIhL/PKLY8dnzw7z5rmnFhERydgUPiTdEhNh40bHzpkzR3e2iIhkVgofkm4vv+zY8a+/rjtbREQyM91qK+litcL8+fYda7GYrZann3ZvTSIikrFp5EPSZe1auHjRvmMnTlTwEBERhQ9JJ3vX58iSBXr1cm8tIiLiGxQ+xGnz58MPP9h37FNPmXe4iIiIKHyIUxxd0fSll9xXi4iI+BaFD3HKL79AfLz9x5844b5aRETEtyh8iMNefx2aNHHsnAIF3FOLiIj4Ht1qKw5p0QKWLHHsnMKFoXZt99QjIiK+RyMfYher1Zw06mjwAHj3Xa1mKiIi1yl8yB199x3kygULFjh+7vz50Lq162sSERHfpfAhtzVwoLkw2JUrjp/bu7eWURcRkdQUPuSW5s+HCROcP79VK9fVIiIi/kPhQ9Lk6DoeN9MkUxERuRWFD0nT6NGOreNxM00yFRGRW1H4kFSsVufbLfnymRNTNclURERuReFDUhk9Gi5ccOychx4yVz397z8FDxERuT0tMiYpWK1my8QRr70GEye6px4REfE/Ch+Swtq1cOaMfcdmzw6zZ5u34oqIiNhL4UNSiImx77gcOSAuzgwgIiIijtCcD0nB3gfADR6s4CEiIs5R+JAUatc21+iwWG59TL58MGSI52oSERH/ovAhKQQEXJ9weqsA8vHHWsNDREScp/AhqbRuDd9+C2FhKfcXKaI1PEREJP0UPiSVyEjo1w9Onry+LywMJk1S8BARkfTT3S6SQmSk+SRaw0i5//RpaNvWbLcogIiISHpo5ENsrFbo0yd18IDr+/r2NY8TERFxlsKH2KxdC0eP3vp1w4AjR8zjREREnKXwITb2LjBm73EiIiJpUfgQG3sXGLP3OBERkbQofIjNnRYYs1jM221r1/ZsXSIi4l8UPsTmdguMJW9PnaoFxkREJH0UPiSF1q3hu++gUKGU+wsXNvfrNlsREUkvrfMhqbRuDS1amHe1xMSYczxq19aIh4iIuIbCh6QpIADq1vV2FSIi4o/UdhERERGPUvgQERERj1L4EBEREY9S+BARERGP8pnw0bx5c4oWLUqOHDkoUKAAHTt25Pjx4ymOiY6OplmzZuTMmZOwsDB69+5NYmKilyoWERGRtPhM+KhXrx7ffvst+/btY8GCBRw4cICnnnrK9rrVauWJJ57g4sWLrFu3jrlz57JgwQJee+01L1YtIiIiN7MYRloPUM/4lixZQsuWLUlISCBbtmwsW7aMJ598kiNHjlCwYEEA5s6dS5cuXThx4gS5c+e267rx8fGEhoYSFxdn9zkiIiJi/89Qnxn5uNGZM2eYM2cONWvWJFu2bABs2LCBihUr2oIHQOPGjUlISGDr1q23vFZCQgLx8fEpvkRERMR9fCp8vPHGG+TMmZN8+fIRHR3N4sWLba/FxsYSHh6e4vg8efKQPXt2YmNjb3nNsWPHEhoaavsqUqSI2+oXERERL4eP4cOHY7FYbvu1ZcsW2/Gvv/4627ZtY/ny5QQEBNCpUydu7BpZ0ngcq2EYae5PNnjwYOLi4mxfR44cce2HFBERkRS8urx6r169ePbZZ297TPHixW2/DwsLIywsjDJlylC+fHmKFCnCxo0bqVGjBhEREWzatCnFuWfPnuXq1aupRkRuFBgYSGBgYLo+h4iIiNjPq+EjOUw4I3nEIyEhAYAaNWowevRoYmJiKFCgAADLly8nMDCQqlWruqZgERERSTefeLDc5s2b2bx5M4888gh58uTh4MGDvPXWW5QsWZIaNWoA0KhRIypUqEDHjh2ZMGECZ86cYcCAAXTr1k13rYiIiGQgPjHhNCgoiMjISOrXr0/ZsmXp2rUrFStWZPXq1baWSUBAAEuXLiVHjhzUqlWLZ555hpYtWzJx4kQvVy8iIiI38tl1PtxF63yIiIg4x6/X+RARERHfpfAhIiIiHqXwISIiIh6l8CEiIiIepfAhIiIiHqXwISIiIh6l8CEiIiIepfAhIiIiHqXwISIiIh6l8CEiIiIepfAhIiIiHqXwISIiIh6l8CEiIiIeldXbBUjGY7XC2rUQEwMFCkDt2hAQ4O2qRETEXyh8SAqRkdCnDxw9en1f4cLw7rvQurX36hIREf+htovYREbCU0+lDB4Ax46Z+yMjvVOXiIj4F4UPAcxWS58+YBipX0ve17eveZyIiEh6KHwIYM7xuHnE40aGAUeOmMeJiIikh8KHALB4sX3HxcS4tw4REfF/Ch+C1QqzZ9t3bIEC7q1FRET8n8KHsHYtnDp15+Py5zdvuxUREUkPhQ+xu5XSoYPW+xARkfRT+BC7WyktWri3DhERyRwUPoTatc2FxCyWWx9TpIhaLiIi4hoKH0JAgLmCKaQOIBaL+TV1qlouIiLiGgofAphLp3/3HRQqlHJ/4cLmfi2tLiIirqJnu4hN69bmvA49VE5ERNxJ4UNSCAiAunW9XYWIiPgztV1ERETEoxQ+RERExKMUPkRERMSjNOdDAPP5LppoKiIinqDwIURGQp8+cPTo9X2FC5trf+gWWxERcTW1XTK5yEh46qmUwQPg2DFzf2Skd+oSERH/pfCRiVmt5oiHYaR+LXlf377mcSIiIq6i8JGJrV2besTjRoYBR46Yx4mIiLiKwkcmFhPj2uNERETsofCRie3fb99xBQq4tw4REclcFD4yqfnzYeTIOx9XuLB5262IiIir6FbbTCgyEp55xr5ju3XTeh8iIuJaGvnIZJLvcLFX6dLuq0VERDInhY9MxGqFF1+8/R0uN9N8DxERcTW1XfxY8pLpx47Br7+a8zwuXLD//CJFNN9DRERcT+HDzyQHjsWLYc4cOHnS+WtNnar5HiIi4noKH34krWe0OCMgAObO1XNdRETEPRQ+/ETyM1rSWirdUd98Y15LRETEHRQ+fJzVCqtWmbfEuiJ4jBgBTz+d/uuIiIjcisKHD0mezxETY96FcuoU9OuX/jZLssKFYcgQ11xLRETkVhQ+fISr5nPcisUC776rCaYiIuJ+Ch8+wJXzOdKSLx98/LEmmIqIiGdokbEMLnlFUncEj1y5zDke//2n4CEiIp6jkY8M5uZ5HVar61stefOagWbIELVZRETE8xQ+MpC05nXkzZu+a+bPD+3aQYkS5u8LFTJXLVXoEBERb1H4yCBuNa/jzBnnrpc3L3z7LdStq6AhIiIZi8JHBuDKeR0Wi/nrJ59A/frpv56IiIiracJpBrB2rWvX6vjuO00gFRGRjEsjHxlATIx9x+XNm7INU6QITJpkzuVInqCq+RwiIpLRKXxkAAUK2Hfct9+awUJBQ0REfJnCh5vdfOtsWoGhdm2zXXLsWNrzPiwW83VNHhUREX+gOR9uFBkJxYtDvXrQvr35a/Hi5v4bBQSYS5vD9QmjyZK3p05V8BAREf+g8OEmybfO3jyR9Ngxc//NAaR1a3OiaKFCKfdrAqmIiPgbi2G464khvik+Pp7Q0FDi4uLInTu3U9ewWs0RjlvdwZLcRomKSj2aYU+bRkREJCOy92eo5ny4wZ1unTUMOHLEPK5u3ZSvBQSk3iciIuJPfK7tkpCQQOXKlbFYLGzfvj3Fa9HR0TRr1oycOXMSFhZG7969SUxM9HiN9t46a+9xIiIi/sTnRj4GDhxIwYIF+euvv1Lst1qtPPHEE+TPn59169Zx+vRpOnfujGEYTJs2zaM12nvrrL3HiYiI+BOfGvlYtmwZy5cvZ+LEialeW758Obt372b27Nk88MADNGjQgEmTJvHJJ58QHx/v0TqTb529+c6VZBaLuUBY7doeLUtERCRD8Jnw8d9//9GtWze++uorgoODU72+YcMGKlasSMGCBW37GjduTEJCAlu3br3ldRMSEoiPj0/xlV66dVZEROTWfCJ8GIZBly5d6N69O9WqVUvzmNjYWMLDw1Psy5MnD9mzZyc2NvaW1x47diyhoaG2ryJFirikZt06KyIikjavho/hw4djsVhu+7VlyxamTZtGfHw8gwcPvu31LGn0OQzDSHN/ssGDBxMXF2f7OnLkSLo/V7LWreHQIVi5Er7+2vw1KkrBQ0REMjevTjjt1asXzz777G2PKV68OG+//TYbN24kMDAwxWvVqlWjQ4cOfPHFF0RERLBp06YUr589e5arV6+mGhG5UWBgYKrrupJunRUREUnJJxYZi46OTjEX4/jx4zRu3JjvvvuO6tWrU7hwYZYtW8aTTz7J0aNHKfD/t5HMmzePzp07c+LECbsXDHPFImMiIiKZkV8tMla0aNEU27ly5QKgZMmSFC5cGIBGjRpRoUIFOnbsyIQJEzhz5gwDBgygW7duChEiIiIZiE9MOLVHQEAAS5cuJUeOHNSqVYtnnnmGli1bpnlbroiIiHiPT7RdPEltFxEREefY+zPUb0Y+RERExDcofIiIiIhHKXyIiIiIRyl8iIiIiEcpfIiIiIhHKXyIiIiIRyl8iIiIiEcpfIiIiIhHKXyIiIiIR/nEs108KXnB1xsfZCciIiJ3lvyz806Lpyt83OT8+fMAFClSxMuViIiI+Kbz588TGhp6y9f1bJebJCUlcfz4cUJCQrBYLLc8Lj4+niJFinDkyBG/fAaMP38+f/5s4N+fz58/G/j35/Pnzwb+/fkc+WyGYXD+/HkKFixIliy3ntmhkY+bZMmShcKFC9t9fO7cuf3uP7Qb+fPn8+fPBv79+fz5s4F/fz5//mzg35/P3s92uxGPZJpwKiIiIh6l8CEiIiIepfDhpMDAQIYNG0ZgYKC3S3ELf/58/vzZwL8/nz9/NvDvz+fPnw38+/O547NpwqmIiIh4lEY+RERExKMUPkRERMSjFD5ERETEoxQ+RERExKMUPlwsISGBypUrY7FY2L59u7fLcYnmzZtTtGhRcuTIQYECBejYsSPHjx/3dlnpdujQIV544QVKlChBUFAQJUuWZNiwYSQmJnq7NJcZPXo0NWvWJDg4mLvuusvb5aTbBx98QIkSJciRIwdVq1Zl7dq13i7JJdasWUOzZs0oWLAgFouFRYsWebsklxk7diwPPvggISEh3H333bRs2ZJ9+/Z5uyyX+PDDD7nvvvtsi2/VqFGDZcuWebsstxg7diwWi4W+ffu65HoKHy42cOBAChYs6O0yXKpevXp8++237Nu3jwULFnDgwAGeeuopb5eVbnv37iUpKYkZM2awa9cupkyZwkcffcSbb77p7dJcJjExkaeffppXXnnF26Wk27x58+jbty9Dhgxh27Zt1K5dm6ZNmxIdHe3t0tLt4sWL3H///UyfPt3bpbjc6tWr6dmzJxs3bmTFihVcu3aNRo0acfHiRW+Xlm6FCxfmnXfeYcuWLWzZsoXHHnuMFi1asGvXLm+X5lJ//PEHH3/8Mffdd5/rLmqIy/z4449GuXLljF27dhmAsW3bNm+X5BaLFy82LBaLkZiY6O1SXG78+PFGiRIlvF2Gy82cOdMIDQ31dhnp8tBDDxndu3dPsa9cuXLGoEGDvFSRewDGwoULvV2G25w4ccIAjNWrV3u7FLfIkyeP8emnn3q7DJc5f/68Ubp0aWPFihVGnTp1jD59+rjkuhr5cJH//vuPbt268dVXXxEcHOztctzmzJkzzJkzh5o1a5ItWzZvl+NycXFx5M2b19tlyE0SExPZunUrjRo1SrG/UaNGrF+/3ktViTPi4uIA/O7/M6vVyty5c7l48SI1atTwdjku07NnT5544gkaNGjg0usqfLiAYRh06dKF7t27U61aNW+X4xZvvPEGOXPmJF++fERHR7N48WJvl+RyBw4cYNq0aXTv3t3bpchNTp06hdVqJTw8PMX+8PBwYmNjvVSVOMowDPr3788jjzxCxYoVvV2OS/z999/kypWLwMBAunfvzsKFC6lQoYK3y3KJuXPn8ueffzJ27FiXX1vh4zaGDx+OxWK57deWLVuYNm0a8fHxDB482Nsl283ez5bs9ddfZ9u2bSxfvpyAgAA6deqEkUEXx3X0swEcP36cJk2a8PTTT/Piiy96qXL7OPP5/IXFYkmxbRhGqn2ScfXq1YsdO3bwzTffeLsUlylbtizbt29n48aNvPLKK3Tu3Jndu3d7u6x0O3LkCH369GH27NnkyJHD5dfX8uq3cerUKU6dOnXbY4oXL86zzz7L999/n+IvQavVSkBAAB06dOCLL75wd6kOs/ezpfUf3dGjRylSpAjr16/PkMOLjn6248ePU69ePapXr86sWbPIkiVjZ3Jn/uxmzZpF3759OXfunJurc4/ExESCg4OZP38+rVq1su3v06cP27dvZ/Xq1V6szrUsFgsLFy6kZcuW3i7FpV599VUWLVrEmjVrKFGihLfLcZsGDRpQsmRJZsyY4e1S0mXRokW0atWKgIAA2z6r1YrFYiFLliwkJCSkeM1RWV1RpL8KCwsjLCzsjse99957vP3227bt48eP07hxY+bNm0f16tXdWaLT7P1saUnOqwkJCa4syWUc+WzHjh2jXr16VK1alZkzZ2b44AHp+7PzVdmzZ6dq1aqsWLEiRfhYsWIFLVq08GJlcieGYfDqq6+ycOFCVq1a5dfBA8zPm1H/bnRE/fr1+fvvv1Pse/755ylXrhxvvPFGuoIHKHy4RNGiRVNs58qVC4CSJUtSuHBhb5TkMps3b2bz5s088sgj5MmTh4MHD/LWW29RsmTJDDnq4Yjjx49Tt25dihYtysSJEzl58qTttYiICC9W5jrR0dGcOXOG6OhorFarbe2ZUqVK2f479RX9+/enY8eOVKtWjRo1avDxxx8THR3tF3N0Lly4wL///mvbjoqKYvv27eTNmzfV3y++pmfPnnz99dcsXryYkJAQ2xyd0NBQgoKCvFxd+rz55ps0bdqUIkWKcP78eebOncuqVav46aefvF1auoWEhKSal5M8788l83Vccs+MpBAVFeU3t9ru2LHDqFevnpE3b14jMDDQKF68uNG9e3fj6NGj3i4t3WbOnGkAaX75i86dO6f5+VauXOnt0pzy/vvvG8WKFTOyZ89uVKlSxW9u11y5cmWaf06dO3f2dmnpdqv/x2bOnOnt0tKta9eutv8e8+fPb9SvX99Yvny5t8tyG1feaqs5HyIiIuJRGb/BLSIiIn5F4UNEREQ8SuFDREREPErhQ0RERDxK4UNEREQ8SuFDREREPErhQ0RERDxK4UNEREQ8SuFDxMccOnQIi8ViWyrdVxQvXpypU6e67Hp169alb9++LrueN1gsFhYtWgT47p+riDMUPkQyEIvFctuvLl26eLvEO5o1axZ33XVXqv1//PEHL730kucLygCGDx9O5cqVU+2PiYmhadOmni9IxMv0YDmRDCQmJsb2+3nz5vHWW2+xb98+276goCDOnj3rjdJSPE7bGfnz53dxRb7PXx5gKOIojXyIZCARERG2r9DQUCwWS6p9yQ4ePEi9evUIDg7m/vvvZ8OGDSmutX79eh599FGCgoIoUqQIvXv35uLFi7bXz549S6dOnciTJw/BwcE0bdqUf/75x/Z68gjGDz/8QIUKFQgMDOTw4cMkJiYycOBAChUqRM6cOalevTqrVq0CYNWqVTz//PPExcXZRmuGDx8OpG67nDt3jpdeeonw8HBy5MhBxYoV+eGHHwA4ffo07dq1o3DhwgQHB1OpUiW++eYbh7+f77zzDuHh4YSEhPDCCy8waNCgFCMQabVuWrZsmWKEafbs2VSrVo2QkBAiIiJo3749J06csL2+atUqLBYLv/76K9WqVSM4OJiaNWvaQuOsWbMYMWIEf/31l+17MmvWLCBl2yUtu3fv5vHHHydXrlyEh4fTsWNHTp06ZXv9u+++o1KlSgQFBZEvXz4aNGiQ4s9YJKNS+BDxUUOGDGHAgAFs376dMmXK0K5dO65duwbA33//TePGjWndujU7duxg3rx5rFu3jl69etnO79KlC1u2bGHJkiVs2LABwzB4/PHHuXr1qu2YS5cuMXbsWD799FN27drF3XffzfPPP8/vv//O3Llz2bFjB08//TRNmjThn3/+oWbNmkydOpXcuXMTExNDTEwMAwYMSFV7UlISTZs2Zf369cyePZvdu3fzzjvvEBAQAMCVK1eoWrUqP/zwAzt37uSll16iY8eObNq0ye7vz7fffsuwYcMYPXo0W7ZsoUCBAnzwwQcOf58TExMZNWoUf/31F4sWLSIqKirN9teQIUOYNGkSW7ZsIWvWrHTt2hWAtm3b8tprr3Hvvffavidt27a94/vGxMRQp04dKleuzJYtW/jpp5/477//eOaZZ2yvt2vXjq5du7Jnzx5WrVpF69at0bNCxSe45Nm4IuJyM2fONEJDQ1Ptj4qKMgDj008/te3btWuXARh79uwxDMMwOnbsaLz00kspzlu7dq2RJUsW4/Lly8b+/fsNwPj9999tr586dcoICgoyvv32W9v7A8b27dttx/z777+GxWIxjh07luLa9evXNwYPHnzbuosVK2ZMmTLFMAzD+Pnnn40sWbIY+/bts/v78fjjjxuvvfaabftOj/euUaOG0b179xT7qlevbtx///23vUaLFi1u+yj7zZs3G4Bx/vx5wzAMY+XKlQZg/PLLL7Zjli5dagDG5cuXDcMwjGHDhqV432SAsXDhQsMwrv+5btu2zTAMwxg6dKjRqFGjFMcfOXLEAIx9+/YZW7duNQDj0KFDt6xVJKPSyIeIj7rvvvtsvy9QoACArR2wdetWZs2aRa5cuWxfjRs3JikpiaioKPbs2UPWrFmpXr267Rr58uWjbNmy7Nmzx7Yve/bsKd7nzz//xDAMypQpk+Laq1ev5sCBA3bXvn37dgoXLkyZMmXSfN1qtTJ69Gjuu+8+8uXLR65cuVi+fDnR0dF2v8eePXuoUaNGin03b9tj27ZttGjRgmLFihESEkLdunUBUtVyuz8PZ2zdupWVK1em+D6XK1cOgAMHDnD//fdTv359KlWqxNNPP80nn3zitflAIo7ShFMRH5UtWzbb7y0WC2C2M5J/ffnll+ndu3eq84oWLcr+/fvTvKZhGLZrgTnB9cbtpKQkAgIC2Lp1q61FkixXrlx21x4UFHTb1ydNmsSUKVOYOnUqlSpVImfOnPTt25fExES738MeWbJkSdWmuLHtdPHiRRo1akSjRo2YPXs2+fPnJzo6msaNG6eq5XZ/Hs5ISkqiWbNmjBs3LtVrBQoUICAggBUrVrB+/XqWL1/OtGnTGDJkCJs2baJEiRJOv6+IJyh8iPihKlWqsGvXLkqVKpXm6xUqVODatWts2rSJmjVrAuYkz/3791O+fPlbXveBBx7AarVy4sQJateuneYx2bNnx2q13ra+++67j6NHj7J///40Rz/Wrl1LixYteO655wDzB/E///xz29puVr58eTZu3EinTp1s+zZu3JjimPz586e4w8hqtbJz507q1asHwN69ezl16hTvvPMORYoUAWDLli1215DMnu/JzapUqcKCBQsoXrw4WbOm/Ve1xWKhVq1a1KpVi7feeotixYqxcOFC+vfv73CNIp6ktouIH3rjjTfYsGEDPXv2ZPv27fzzzz8sWbKEV199FYDSpUvTokULunXrxrp16/jrr7947rnnKFSoEC1atLjldcuUKUOHDh3o1KkTkZGRREVF8ccffzBu3Dh+/PFHwLyr5cKFC/z666+cOnWKS5cupbpOnTp1ePTRR2nTpg0rVqwgKiqKZcuW8dNPPwFQqlQp27/q9+zZw8svv0xsbKxD34M+ffrw+eef8/nnn7N//36GDRvGrl27Uhzz2GOPsXTpUpYuXcrevXvp0aMH586ds71etGhRsmfPzrRp0zh48CBLlixh1KhRDtWR/D2Jiopi+/btnDp1ioSEhDue07NnT86cOUO7du3YvHkzBw8eZPny5XTt2hWr1cqmTZsYM2YMW7ZsITo6msjISE6ePOlQQBPxFoUPET903333sXr1av755x9q167NAw88wNChQ21zEQBmzpxJ1apVefLJJ6lRowaGYfDjjz+maB+kZebMmXTq1InXXnuNsmXL0rx5czZt2mQbGahZsybdu3enbdu25M+fn/Hjx6d5nQULFvDggw/Srl07KlSowMCBA22jA0OHDqVKlSo0btyYunXrEhERQcuWLR36HrRt25a33nqLN954g6pVq3L48GFeeeWVFMd07dqVzp0706lTJ+rUqUOJEiVsox5gjozMmjWL+fPnU6FCBd555x0mTpzoUB0Abdq0oUmTJtSrV4/8+fPbddtwwYIF+f3337FarTRu3JiKFSvSp08fQkNDyZIlC7lz52bNmjU8/vjjlClThv/9739MmjRJi5aJT7AYNzc8RUT81PDhw1m0aJGWMBfxMo18iIiIiEcpfIiIiIhHqe0iIiIiHqWRDxEREfEohQ8RERHxKIUPERER8SiFDxEREfEohQ8RERHxKIUPERER8SiFDxEREfEohQ8RERHxqP8D62bURhXxdn0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the QQ plot\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "res = stats.probplot(cauchy_sample_means, plot=ax, fit=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02976c76",
   "metadata": {},
   "source": [
    "As you can see, this is very different from a straight line which let's you know that the sample means do not distribute normally. But what if you used a much bigger `sample_size`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "87f1b975",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cauchy_sample_means = sample_means(cauchy_population, sample_size=100)\n",
    "\n",
    "# Create the QQ plot\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "res = stats.probplot(cauchy_sample_means, plot=ax, fit=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1ebed71",
   "metadata": {},
   "source": [
    "Even when using a `sample_size` of 100, which might be unrealistic in real-life scenarios you still don't achieve normality for the sample means. This is important because it is a fact that the central limit theorem does not hold for all distributions and that is a limitation to consider when applying it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "930df17b",
   "metadata": {},
   "source": [
    "**Congratulations on finishing this lab!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "463e6f4a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
